naps.2010.5619585

Abstract—Permanent magnet synchronous generators
(PMSGs) are commonly used as a variable speed generator in
wind energy systems. This paper describes a maximum power
point tracking (MPPT) scheme for a PMSG-based wind energy
conversion system (WECS) in which a buck-boost converter is
used to handle a wide range of wind speeds. A closed-loop with a
PWM inverter forces the WECS to extract the maximum power
available from the wind turbine by shifting the phase angle of
output voltage at a given wind speed. The output power is fed to
the grid. The mathematical model of the wind power system is
built and simulated by MATALB/SIMULINK software.
Simulation results show that the proposed control scheme has a
good dynamic performance and operates the wind generation
system with the maximum efficiency.
Index Terms—maximum power point tracking, permanent
magnet synchronous generator, phase shift, pulse width
modulation, wind energy
I. INTRODUCTION
ARIABLE-SPEED wind generation systems make it
possible to extract the maximum energy from wind with
widely varying speeds. The permanent magnet synchronous
generators (PMSGs) are suitable for small variable-speed wind
turbine generator systems. The wind generation system with a
PMSG represents one important trend of development for
wind power applications with numerous advantages like
higher efficiency due to the absence of field copper loss, lower
operating speed due to higher number of poles with smaller
pole pitch, and the elimination of gearbox [1], [2]. Smaller
wind turbines use fixed pitch angle without the need for
additional pitch control. The power from the wind energy
conversion system (WECS) is normally fed to an ac grid.
Like in any wind power system, it is desirable to extract the
maximum power available at a given wind speed. There are
different methods used to extract the maximum power from
the wind. Different control concepts for maximum power
point tracking (MPPT) in WECS with PMSG are described
and the performance for each is compared in [3]. The MPPT
methods can be broadly classified as those which use sensors
and those which do not use sensors. They are also classified
based on the type of control, such as fuzzy logic based control
[4] and sliding mode control [5].
Xin Wang and S. Yuvarajan are with the Department of Electrical and
Computer Engineering, North Dakota State University, Fargo, ND 58108
USA (email: [e-mail]; [e-mail]).
Lingling Fan is with the Department of Electrical Engineering, University
of South Florida, Tampa, USA (email: [e-mail]).
To convert the variable-frequency output voltage from the
PMSG into an ac voltage of the grid frequency (60Hz), two
typical power converter topologies for small wind turbine
systems with PMSG are presented and explained in [6]. The
first configuration uses a diode-bridge rectifier, a boost
converter and an inverter; and the second configuration uses a
back-to-back converter system. The MPPT is implemented on
the dc-dc converter in the former system and on the PWM
inverter in the latter one. In the dc-dc converter, the duty cycle
is controlled, and in the PWM inverter the modulation index is
controlled, for MPPT. An input-output feedback linearization
(IOL) technique is applied to design the high-performance
nonlinear current controller on the PWM rectifier in [7]. A
sensorless MPPT control strategy on the PWM inverter is
implemented in [8], which is achieved without a wind speed
sensor and mechanical sensors such as rotor speed sensor and
position sensor. A new variable-speed WECS with a PMSG
and Z-source inverter is proposed in [9]. Compared to the
conventional WECS with boost converter, the number of
semiconductor switches used in [9] is reduced by one and the
system reliability is improved. Another nonlinear approach for
MPPT is also presented in [10]. It uses a matrix converter and
the controller is based on the nonlinear adaptive backstepping
method which is able to effectively accommodate the effects
of system uncertainties.
The paper proposes an MPPT scheme for a WECS with a
PMSG. The major advantage of using a PMSG is its ability to
handle a wide range of rotor speeds which correspond to a
large range of wind speeds. In a PMSG, the frequency and
amplitude of the output voltage vary with wind speed. In order
to maintain a narrow range of dc link voltage, the proposed
wind generation system uses a dc-dc converter with buck-
boost feature which can step up or step down the rectified
voltage by controlling its duty cycle. Also, in the PWM
inverter, another closed-loop is designed to accurately track
the maximum power point by shifting the phase angle of the
output voltage with respect to that of the grid voltage.
II. DESCRIPTION OF THE WECS SET UP
The functional block diagram of the proposed wind energy
MPPT system is shown in Fig. 1. The wind speed measured
using an anemometer is utilized to compute the maximum
MPPT Control for a PMSG-Based Grid-Tied
Wind Generation System
Xin Wang, Subbaraya Yuvarajan, Senior Member, IEEE, and Lingling Fan, Senior Member, IEEE
V

Wind
Turbine
Wind Speed
ωm
PMSG
Three-phase
Diode
Rectifier
PI
Three-phase
PWM Inverter
Vdc
PWM
Modulator
Power
Calculator
_
Gate Pulse
Generator PI _
Vdcref
Pmax Pout
Vw
Vrec
Vgrid
Igrid
Grid
*
Tm
Buck-Boost Converter
Duty Cycle
Fig. 1. Block diagram of proposed MPPT system
power Pmax* which is used as the reference for the outer power
control loop. While extracting maximum power, the wind
turbine runs the PMSG at the optimum speed ωm. The three-
phase variable frequency output voltage from the PMSG is
rectified using a three-phase diode rectifier and fed as the
input to the buck-boost dc to dc converter. At any wind speed,
the output voltage of the buck-boost converter Vdc can be
regulated at a constant level by controlling the duty cycle of
the active switch through a PI controller as shown in Fig. 1.
The reference voltage Vdcref is chosen to match of the output of
the PWM inverter which will be the grid voltage. The use of a
buck-boost converter allows the WECS to operate over a wide
range of wind speeds (very low to very high) but within the
permissible limits.
The output of the buck-boost converter is fed to the
PWM inverter whose reference sine input is taken from the
grid. Keeping the modulation index constant, the phase of the
inverter output voltage can be shifted using a feedback loop.
This done by comparing the reference power Pmax* and the
real power that is fed to the grid. A second PI controller
modifies the angle between the grid voltage and corresponding
current in the same phase. By varying the phase angle, the
proposed system can extract maximum power from the wind
turbine and supply the grid.
III. MATHEMATICAL MODEL
A. Wind Turbine
The mechanical power output from the wind turbine is
given by [1]
13
2
mpw
PACV ρ = (1)
where ρ is the air density, A is the sweep area of the turbine
blades, Vw is wind speed, Cp is the aerodynamic power
coefficient which is a function of the pitch angle
β
and the
tip speed ratio
λ . Since
ρ
and
A
are constant parameters, the
wind turbine can produce maximum power under a certain
wind speed only when the turbine operates at the maximum
Cp. A generic equation is used to express Cp. This equation,
based on the turbine characteristics of [11], is given by
()
5
2
134 6
,i
C
p
i
C
CCCCeC
λ
λ
ββ
λ
λ
−
⎛⎞
=−− +
⎜⎟
⎝⎠
(2)
with
3
110.035
0.08 1
i
λλ β
β
=−
++ (3)
where
β
is blade pitch angle, and λ is defined by
m
w
R
V
ω
λ
=. (4)
In (4), m
ω is the turbine angular velocity and R is the turbine
radius. In small wind turbine generation systems,
β
is rarely
changed.
Fig. 2. p C λ − curve of the wind turbine
Fig. 2 shows the p
C
λ
− curve described by (2) for the wind
turbine considered in this paper. From Fig. 2 and the definition
of
λ , at a specific wind speed, there is a unique wind turbine
shaft speed to achieve the maximum power coefficient maxp
C.
When
p
C is controlled to be at its maximum value, the
maximum mechanical power is extracted from the wind
energy for any wind speed.
B. PMSG
The steady-state-induced voltage and torque equations of a
PMSG are given by

3
et
TKI= (5)
em
EK ω = (6)
The mechanical characteristics of the PMSG can be described
by
()
1
mmem
dTTF
dt J
ωω =−− (7)
where J is combined inertia of the rotor and load, Tm is the
mechanical torque input from the wind turbine, Te is
electromagnetic torque, and F is the combined viscous friction
of the rotor and load.
In the simulation, an alternate model for the PMSG is used.
For this, the output voltage of the PMSG at any given speed
and output current is obtained from the experimental
characteristics. Fig. 3 shows the illustrative characteristics of
the phase voltage as a function of load current at different
speeds. The drop in the speed with load current represents the
internal drop of the PMSG which is partly due to the winding
impedance. The per-phase output voltage is given by
Fig. 3. Illustrative characteristics of the phase voltage as a function of load
current at different speeds
12
-
mrm
VK KI ω = (8)
where K1 is a constant for the PMSG calculated from the
experimental characteristics, K2 is the equivalent impedance
constant, and Im is the amplitude of the sinusoidal current
drawn from the PMSG. The rms value of the line-line voltage
from the PMSG is given by
3
2
llrms m
VV=
. (9)
C. Diode rectifier
The output from the PMSG is rectified using a three-phase
rectifier whose output voltage Vrec is given by [12].
32
rec llrms
VV
π
=
(10)
If ignore the losses of diodes, diode rectifier does not change
the power. It only uses to convert ac to dc.
D. Buck-boost Converter
Fig. 4. Power circuit of Buck-boost converter
The rectified voltage Vrec is stepped up/down by the buck-
boost converter (Fig. 4) whose output voltage Vdc and output
current Idc are given respectively by
1
dc rec
D
VV
D
=− − (11)
1
dc rec
D
II
D
−
= (12)
where D is the duty cycle. The inductor is designed to have
continuous current. From the above expression, it can be seen
that the polarity of the output voltage is always negative as the
duty cycle goes from 0 to 1. Apart from the polarity, this
converter is capable operating either the step-up mode (as a
boost converter) or step-down mode (as a buck converter). In
order to obtain a constant dc output voltage, the difference
between the desired output voltage and the actual output
voltage is used to vary the duty cycle of the buck-boost
converter under different wind speeds. It is worth noting that
buck-boost converter maintains a constant power like other dc
to dc converter, when the losses are neglected.
E. PWM Phase shift Control
The buck-boost converter along with the voltage control
loop supplies a constant dc voltage to the three-phase PWM
inverter as shown in Fig. 5.
Fig. 5. Block diagram of PWM phase-shift controller
The PWM inverter converts a dc voltage into a three-phase
ac voltage which is applied to the grid through smoothing
inductors including their parasitic resistors. The currents
flowing into the grid along with the inverter output voltages
are measured for actual power calculation. In order to have a
phase-shift angle with respect to the grid voltage, another PI
controller is utilized. The PWM circuit compares the phase-
shifted reference sine wave (obtained from both the grid and

4
the PI controller) and a high-frequency triangular wave with a
large frequency modulation index mf = ft/f and a nominal
amplitude modulation index ma = Vgird/Vt where ft and Vt are
the frequency and amplitude of the triangular wave
respectively, and f (60Hz) and Vgrid are the frequency and
amplitude of the phase-shifted reference sine wave from the
grid. The PWM inverter provides a three-phase output with
voltage inv
vand current inv i. The relation between vinv and vdc is
given by [12]
0.612
invllrms a dc
VmV= (13)
where Vinvllrms is the rms value of the line-to-line voltage.
If both the three-phase PMSG and three-phase grid operate
under balanced steady-state conditions, and the instantaneous
grid terminal voltage in phase A is gridan
vV δ =∠ (line-to-
neutral voltage), the equation for invan
v will be
()
invan
vV δα
′
=∠+ (14)
where V′ is the amplitude of inverter output voltage and
α is
the phase shift angle provided by the PI controller. According
to equation (9), if ma is fixed and Vdc is maintained constant,
V′ will also be constant. If the per-phase impedance of the
line filter is Z
θ ∠, the current fed to the grid by phase A can
be expressed as
()
invan gridan
grida
vv VV
iI
ZZ
δα δ
β
θθ
′
−∠+ −∠
== =∠
∠∠. (15)
Under balanced operating conditions, the total power to the
grid 3
P
φ
is given by [13]
()
33
g
ridan grida gridbn gridb gridcn gridc
P
pt v i v i v i
φφ
== + +
()
3cosVI δ
β
=− (16)
where
()
3
p
t
φ
is the instantaneous power delivered by all three
phases.
Equation (16) shows that the average power is equal to the
total instantaneous power delivered to the grid which can be
easily calculated using measured three-phase currents and
voltages. In addition, equation (16) shows that the actual
power is not a function of time, but depends on vectors
g
ridln
v
and
g
rid
i. The phase-shift control strategy varies the phase
angle of the inverter output voltage while keeping its
amplitude constant at V′ (the amplitude of grid voltage). The
line impedance in each phase is a constant as well. Besides,
δ
is the phase angle of grid which cannot be varied. From (14),
(15), and (16), it is seen that 3
P
φ
can be varied by varying the
phase-shift angle
α .
IV. MPPT PRINCIPLE
Optimal operation of the PMSG-based WECS is to extract
the maximum power from wind. According to (1), the
maximum power at a given wind speed can be extracted when
Cp, which is a function of the pitch angle
β
and the tip speed
ratio
λ , is maximum. Since
β
is fixed, λ has to be at its
optimal value. From equation (4), it is seen that
λ can be
regulated by changing the turbine angular velocity m
ω . Thus,
the optimal control of the WECS means that the system has to
operate at the optimal value of the rotating speed of the PMSG
at different wind speeds.
Fig. 6. Mechanical power versus rotating speed
for different wind speeds
Fig. 6 represents the relation between generator speed and
output power for different wind speeds. It is seen that the
maximum power output occurs at different rotating speeds for
different wind speeds. The role of the MPPT control strategy
is to track the maximum power curve shown in Fig. 6.
Fig. 7. Vector representations of inverter output current and voltage
without and with phase-shift control
The vector representation of equation (15) is shown in Fig.
7. Fig. 7(a) shows the case without phase-shift control while
Fig. 7(b) shows the case with phase-shift control. It is obvious
that the value of VV
′
− in Fig. 7(a) is smaller than that in Fig.
7(b). Since Z is a constant parameter of the circuit, the output
current in the system without phase-shift control is smaller
than that of a system with phase-shift control. Initially, if the
system operates at a higher value of ωm, then Pm* will be
higher than the actual power which increases the phase shift.
As a result, the output current will increase. When the output
current increases, the input current of the inverter should also
increase because of conservation of energy (neglecting the
losses in the inverter). From equation (12), the output current
of the diode rectifier also increases, which leads to an increase
in the PMSG current. Since the PMSG current is proportional
to electromagnetic torque Te, Te is raised as well. Then the
value of m
d
dt
ω
decreases as in equation (7), which means the
PMSG decelerates and settles down at the optimum ωm which
is lower than the initial speed.
V. SIMULATION RESULTS
The model of the PMSG-based variable-speed wind turbine
system in Fig. 1 is built mainly using Matlab/Simulink
dynamic system simulation software for simulating the

5
behavior of the entire system subjected to wind speed
variations. The simulation model is developed for a 500W
industrial permanent magnet synchronous alternator. The
parameters of the turbine and the PMSG used are given in
Table I. The power converters and both the duty cycle and
phase-shift control algorithms are also implemented in the
model. The sampling time used for the simulation is 10μs. The
wind speed waveform is simulated by TurbSim software based
on the data for the state of North Dakota in US published by
the Department of Energy's Wind Program and the National
Renewable Energy Laboratory (NREL) [14].
TABLE I
PARAMETER OF THE TURBINE-GENERATOR SYSTEM
WIND TURBINE
Air Density (
ρ
) 1.25 kg/m3
Radius of the Turbine Blades ( r ) 0.525 m
PMSG
Rated Voltage, phase 115 V
Rated Output 500 VA
Rated Speed 3428 rpm
Rated Frequency 400 Hz
Stator Phase Resistance ( Rs) 1.57 Ω
Inductances ( Ld=L
q
) 3.51 mH
Inertia ( J ) 0.0008 kg.m2
Friction Factor ( F ) 0.00005 N.m.s
Pole Pairs 7
K1 ( in equation 6 ) 0.0353 V/(rad/s)
K2 ( in equation 6 ) 1.939 Ω
BUCK-BOOST CONVERTER
L 5 mH
C 220 μF
PWM MODULATOR
Amplitude Modulation Index 0.8
Frequency of Triangular Wave 1200 Hz
The operation of the MPPT scheme for a wind speed profile
with step changes is shown in Fig. 8 where the wind speed and
output power are plotted. Fig. 9 shows the variation of rotating
speed and the phase-shift angle which is controlled as
expected. The sight overshoot in the response of the PMSG’s
rotating speed m
ω shows that the controller parameters are set
properly. From both these responses, it is seen that the phase-
shift control system can extract the maximum power from
wind even when the wind speed changes sharply.
Instead of a stepped wind speed, a variable wind speed is
given as a practical one. In order to ensure supplying a
constant input voltage (higher than grid voltage) to the phase-
shift closed-loop, duty cycle is regulated in buck-boost
converter.
Fig. 8. Plot of stepped wind speed profile,
maximum power Pmax* and output power P
Fig. 9. Waveforms of rotating speed of PMSG and phase shift angle
Instead of the stepped wind-speed profile, the system is
tested with a practical profile. Fig. 10 shows the plot of the
wind speed profile which is simulated by TurbSim software
for the wind speed levels in North Dakota state, the
corresponding maximum power Pmax* calculated from the
wind speed, and the actual power P fed to the grid. It is seen
that the actual power tracks the maximum power very well in
the higher wind speed range. However, some sharp variations
are not tracked quite well. That is because of the delay in the
phase-shift controller which is found to be somewhat higher
when achieving robustness. The whole system could be
unstable when there are sharp transitions in the wind speed.
The balancing of the rotating speed and the torque in the
PMSG is the key point in MPPT. The torque is varied
following the changes in the wind speed. The phase-shift
control strategy implements the regulation of the rotating
speed m
ω
in PMSG by shifting the phase angle which is
shown in Fig. 11.
The duty cycle of the buck-boost converter is controlled to
give a constant dc link voltage to the grid. In Fig. 12, the
variation of duty cycle for the wind speed profile of Fig. 10 is
shown and it stays around 0.57. As a result, the output voltage
is kept constant at 250V as shown in Fig. 12.